it includes minimal use of materials and energy 
 per unit product or service ; minimum cost of environmental remediation 
 or waste treatment ; and consistent product quality , eliminating or 
 minimizing off - specification material . energy efficiency and product 
 quality are the two aspects of process performance that can be affected 
 by improvements in process control . understanding process behavior , 
 implemented in a robust model , enables the maximum and safe utilization 
 of the heating / cooling capacity of plants , and sensing and characterizing 
 product quality during the manufacturing process enables real - time 
 optimization of process parameters that maximize quality and throughput 
 simultaneously . this requires implementation of real - time model - based 
 predictive control , which , in recent years , has received a significant 
 boost through progress in computing , modeling , sensor technologies , 
 and chemoinformatics . however , significant challenges remain in implementing 
 model - based predictive controllers , especially in situations when 
 product quality and/or process parameters are difficult to observe 
 directly and require soft sensors in addition to hard sensors . here , 
 we define a soft sensor as a model that receives hard sensor measurements 
 and computes parameter(s ) enabling the determination of process state 
 variables . is frequently used in industry and is challenging 
 and interesting for in situ monitoring , because of time - course variations 
 in concentrations and the gradual change of physical properties within 
 the system . semibatch polymerization , typically performed in the monomer - starved 
 regime , provides an additional challenge for in situ monitoring because 
 of the low concentrations of the monomers . yet , for the complete description 
 of a reaction , it would be highly desirable to know the concentrations 
 of all monomers and reagents in all phases and to have real - time measurements 
 of product quality . at a minimum , it is desirable to be able to measure 
 the particle size distribution as a measure of product quality . at present , it is impossible to devise a measurement technique 
 that would determine monomer concentration in the latex phase . in 
 situ information about an emulsion polymerization process is currently 
 ( industrially ) obtained by a few hard sensors measuring the temperature , 
 the pressure , and the flow of the cooling medium . information about 
 the heat balance is evaluated on the balance of these measurements . however , the polymerization rate of the monomers and the individual 
 monomer concentrations are not observable from the overall heat rate . similarly , in situ monitoring of the particle 
 size distribution 
 is not currently feasible at present . for particle size measurements , a few online sensors are available , such as turbidity meters , photon 
 density wave ( pdw ) probes , focused - beam 
 reflectance measurement ( fbrm ) probes , ultrasound sensors , fiber - optic quasielastic light scattering ( foqls ) , and attenuated - total - reflection infrared ( atr - ir ) spectroscopy . for a critical review of different techniques for monitoring latex 
 particles , thus , at present , robust and reliable hard sensors 
 that would provide in situ measurements of product quality in an emulsion 
 copolymerization process do not exist . to overcome the lack 
 of observability it has already been successfully demonstrated 
 for monitoring the conversion of individual monomers in emulsion polymerization . an immersion raman probe positioned in the bulk of a reaction mixture 
 samples the continuous phase with dispersed particles of monomer(s ) 
 and polymer , thus providing a global measure of monomer concentration(s ) . 
 the ability to measure monomer concentrations with raman spectroscopy 
 depends strongly on their scattering intensities and the spectral 
 overlap between components of a reaction mixture . raman scattering data were also shown to be useful in measuring 
 particle sizes of inorganic nanoparticles . it would be 
 beneficial to combine the ability to measure monomer concentrations 
 and particle sizes with a single in situ probe . developed 
 a method for determining particle size during 
 emulsion polymerization using fourier transform ( ft ) raman spectroscopy 
 combined with multivariate data analysis . this method was tested on different particle sizes with different 
 monomer ratios and showed good agreement between the statistical model 
 and the measured particle sizes . however , this method was tested offline 
 using polymer dispersions of different sizes , rather than in a reaction . furthermore , in a different study , a partial least - squares ( pls ) model 
 of a full spectrum ( 4004000 cm ) was shown 
 to predict particle sizes in a polymerization process . however , it is also known that information about 
 particle vibrations and vibrations of the chain expansion is restricted 
 to low wavenumbers ( < 400 cm ) . thus , a more detailed study of raman scattering in emulsion polymerization 
 is justified . inspired by the huge impact of the copolymerization 
 of styrene 
 and butyl acrylate on industry and research , we studied mainly this two - monomer system . herein , we present the 
 feasibility of the measurement of both monomer conversion and particle 
 size using a single immersed raman probe in batch emulsion copolymerization . 
 several calibration techniques are compared for measurements of both 
 concentration and particle size . furthermore , we correlate predictions 
 of particle size with spectral shift in the low - wavenumber region 
 of raman spectra . styrene 
 ( st , aldrich , 98% ) , butyl acrylate 
 ( ba , sigma - aldrich , 99% ) , methyl acrylate ( ma , aldrich , 99% ) , acrylic 
 acid ( aa , aldrich , 99% ) sodium dodecylbenzenesulfonate ( sdbs , sigma , 
 99% ) , and potassium persulfate ( kps , aldrich ) were all used as received . polymerization was performed 
 under a nitrogen atmosphere in a 0.5 l double - jacketed glass reactor 
 ( radleys ) , equipped with a four - blade turbine impeller , set at 300 
 rpm in all experiments . the temperature of the reaction mixture was 
 maintained using a cryo - compact circulator ( cf41 julabo ) . in a typical 
 batch experiment , the reaction temperature was 60 c , the total 
 amount of monomer was 15 wt % , and 3 wt % sdbs and 0.63 wt % kps with 
 respect to the overall amount of monomers were added . three molar 
 ratios between styrene and butyl acrylate ( st / ba ) were used , namely , 
 50:50 , 80:20 , and 87:13 , and are specified in the results . in the 
 case of the four - monomer copolymerization , the monomer ratios were 
 always styrene / butyl acrylate / methyl acrylate / acrylic acid = 0.73:0.18:0.05:0.05 . the monomer mixture , water , and surfactant were combined and flushed 
 with nitrogen for 1 h before being heated to the reaction temperature . 
 after reaching the reaction temperature , the deoxygenated initiator 
 solution was added to the reaction mixture to start the reaction . conversion of monomers was monitored by offline gas chromatography 
 ( gc ) and in situ raman measurements . to determine monomer conversion 
 by gc , 0.5 ml of the reaction mixture was added to 5 ml of thf , and 
 0.05 ml of toluene was added as an internal standard . the sampling 
 method ensured that all monomer was sampled regardless of its distribution 
 between different reaction phases . simulations of the raman 
 spectra of polystyrene were performed using spartan 14 ( v. 1.1.14 ) 
 for oligomer chains with up to five monomer units . the calculations 
 were carried out in the equilibrium ground - state geometry with hartree a shimadzu gas 
 chromatograph ( gc-2014 ) 
 equipped with a capillary column ( factorfour vf , 1 ms for a 15-m length 
 and 0.25-mm i.d . , 0.25-m film thickness , varian ) and flame 
 ionization detector was used for monitoring conversion of the monomers . the raman spectrometer ( horiba jobin yvon labram hr ) was equipped 
 with an olympus bx41 microscope ( 10 objective ) and a superhead 
 fiber probe with 10-m - long fibers and a semispherical immersion probe 
 with sampling depth of several micrometers . raman spectra 
 were excited by a nd : yag laser ( 532.8 nm , 16 mw ) at a nominal resolution 
 of 46 cm in the range between 150 and 
 1800 cm . the acquisition was repeated four times 
 with an exposure time of 8 s. repeated acquisitions were performed 
 to improve the signal - to - noise ratio . peaxact software ( supplied by 
 s - pact ) was used for data analysis . dynamic light scattering 
 ( dls ) was measured on a malvern zetasizer 
 nano s90 instrument at a concentration of approximately 1 mg ml . two measurements of 12 subruns each were obtained 
 at a 173 backscatter measuring angle , equilibrated at 25 c . all 
 spectra were normalized to the intensity of the 1000 cm band to reduce the influence of phenomena other than bond formation 
 on the raman signal intensity . the models were calibrated on 52 spectra 
 of different emulsion copolymerization reactions , where the monomer 
 ratio was kept constant but the reaction temperature was varied between 
 60 and 90 c to show the potential of the calibration model . for peak integration ( pi ) , the 16101690 cm peak area was chosen , which includes the vinyl groups of both styrene 
 and butyl acrylate . although additional areas were added to the model , 
 no improvement was achieved , and only this spectral range was used 
 for pi model . for the indirect hard model ( ihm ) and the partial least - squares 
 ( pls ) model , the entire normalized spectra were taken into account . the indirect hard model ( ihm ) was 
 built with the pure - component spectra of styrene , butyl acrylate , 
 and the copolymer . the number of peaks was chosen depending 
 on the error of the hard model fit to the spectra . root - mean - square 
 errors ( rmses ) below < 0.1 were considered acceptable . table 1 reports the results 
 of the calibration of 52 spectra compared with offline gc data . for 
 the pls model , a multivariate regression function root - mean - square error of cross - validation . for predicting particle 
 size , only a statistical method , specifically 
 the partial least - squares ( pls ) model , was used . the first model , model 8 , considered 
 the spectral range of 150400 cm and included 
 a baseline correction with a linear - fit subtraction . for model 9 , the same spectral range , 150400 cm , was 
 used , but it was normalized to the intensity of 1000 cm band . model 10 included a linear baseline 
 correction , whereas model 11 additionally used normalized spectra . in the case of 
 the copolymerization of styrene and butyl acrylate , 
 the stretching vibrations of the vinyl group in the two monomers appear 
 at 1631 and 1639 cm , respectively . as a result of this overlap , the band corresponding 
 to the vinyl group can not be associated with a specific monomer . furthermore , 
 butyl acrylate does not have many other significant bands ( see supporting information , figure s1 ) . when used 
 in a styrene / butyl acrylate molar ratio of 80:20 or greater , the determination 
 of butyl acrylate by raman spectroscopy is problematic because of 
 a low signal intensity and significant spectral overlap . spectral overlap and low scattering , 
 leading to significant errors 
 in quantitative concentration determinations , are well - known problems 
 of in situ optical spectroscopy . in the case of emulsion polymerization , an additional complication is the observed decrease in intensity of 
 the entire spectrum in the early phase of reaction ( see supporting information , figure s2 ) . such a decrease 
 was reported earlier and was linked to the onset of polymerization , or less light being 
 collected because of scattering by forming and growing latex particles . however , for the determination of monomer concentrations , the effect 
 of variable scattering is detrimental and , therefore , was eliminated 
 by normalizing the overall spectra to the intensity of the 1000 cm band , corresponding to the breathing mode of the 
 phenyl group . for the prediction of monomer concentrations , three different methods 
 were used initially : peak integration ( pi ) , partial least - squares 
 ( pls ) , and indirect hard modeling ( ihm ) . the peak integration model 
 was able to predict only the overall conversion and was found to be 
 unreliable in predicting the concentration of each monomer because 
 of the high spectral overlap . however , to increase the observability 
 of the system , it is unsatisfactory to estimate the overall conversion 
 alone . rather , it is highly desirable to quantify the concentrations 
 of the individual monomers . the pls model was found to slightly 
 underestimate the conversions 
 of the monomers at the beginning of the reaction but to fit well the 
 offline measurements toward the end of the reaction ( see figure 1 ) . in the first few 
 minutes of a reaction after addition of the initiator , the process 
 is influenced by nucleation , the shrinking of the monomer droplets , 
 and the formation of particles . although the spectra were normalized 
 to decrease this effect , the disturbance introduced by the rapid change 
 in the physical properties of the system apparently translates into 
 errors in the quantification of concentrations at the beginning of 
 the reaction . conversions of styrene and butyl acrylate for st / ba monomer 
 ratios 
 of ( a ) 80:20 and ( b ) 87:13 predicted using the pls model compared 
 with offline gc data . the ih model was found to poorly describe the concentration 
 profile 
 of butyl acrylate ( figure 2 ) . this model was built from the spectra of all three components : 
 styrene , butyl acrylate , and copolymer . in addition , the low 
 ratio of butyl acrylate in the studied system further reduced the 
 accuracy of its quantification . as a result , ihm overestimates the 
 concentration of butyl acrylate at the beginning of polymerization . 
 of particular interest in ihm is the adjustment of the component weight 
 parameters based on the analysis of the concentration of each component . each model parameter is automatically 
 adjusted until the hard model fits a certain measured spectrum . however , normalization might affect the weighting 
 of the single spectra and might be one reason for the poor prediction 
 of the butyl acrylate concentration . conversions of styrene and butyl acrylate 
 for st / ba monomer ratios 
 of ( a ) 80:20 and ( b ) 87:13 predicted using the ih model compared with 
 offline gc data . in the case of the emulsion 
 copolymerization of styrene and butyl 
 acrylate , the pls model describes the conversions of the two monomers 
 better than the ihm . however , in general , pls models are limited to 
 their calibration range . in the case of such a complex process as 
 emulsion polymerization , changes in process conditions or composition , 
 such as substitution of the surfactant or monomers , would require 
 retraining of the pls calibration model to enable in situ monitoring 
 of the monomers . to investigate the robustness of the obtained 
 pls calibration model 
 for monomer concentrations , predictions of the concentrations were 
 performed with pls models calibrated with data obtained at different 
 monomer ratios . thus , predictions of the concentrations in an experiment 
 with a styrene / butyl acrylate ratio of 80:20 were performed with a 
 pls model calibrated on the data obtained with a 50:50 monomer ratio , 
 and vice versa . these experiments also tested the significance of 
 intermolecular interactions within this system in pls calibration 
 models . figure 3 shows the 
 predictions of the polymerization reaction for the monomer ratio of 
 80:20 with a model calibrated for a 50:50 ratio . these predictions 
 are surprisingly good for a model not trained on the specific monomer 
 ratio : the pls model describes the conversion profile well , whereas 
 ihm does not predict the butyl acrylate concentration . the same was 
 done in reverse , with a model calibrated on the 80:20 training data 
 used to predict the conversions in an experiment with a 50:50 monomer 
 ratio , and good agreement was found ( supporting information , figure s11 ) . however , the predictions of the conversions 
 at the start of the reaction were slightly deteriorated compared to 
 those of models trained on the correct monomer ratios ( see figure 1 ) . this still implies 
 the need for more extensive model calibration at the early stages 
 of the reaction and for the specific monomer ratios . a good 
 prediction by a statistical model outside its calibration 
 range suggests a low contribution of intermolecular interactions to 
 the spectra . such interactions would normally make it impossible to 
 extend the range of a statistical model beyond its training set . prediction 
 of conversion in an experiment using a 80:20 styrene / butyl 
 acrylate monomer ratio using models calibrated on a 50:50 monomer 
 ratio : ( a ) pls model and ( b ) ihm . a system more relevant to many industrial polymerization 
 processes 
 would involve more than two monomers , for example , a four - monomer 
 system . we evaluated the feasibility of developing a spectral calibration 
 model for a four - monomer system including acrylic acid , methyl acrylate , 
 styrene , and butyl acrylate . the similar structures of the acrylic monomers chosen for 
 the four - monomer 
 system are reflected in the raman spectra . the overlapping of the 
 bands is significant and results in a highly inaccurate prediction 
 model . for industrial relevance , the amounts of the water - soluble 
 monomers , acrylic acid and methyl acrylate , should remain at < 8 
 wt % . at such low concentrations of the water - soluble monomers , we 
 were unable to develop calibration models for these monomers , because 
 of low signal - to - noise ratios and significant overlap of key bands . hence , predictions of the conversions of the individual monomers in 
 this system by raman spectroscopy still remain challenging . only the 
 overall conversion was predicted , as shown in figure 5 . overall conversions of emulsion copolymerization 
 predicted with 
 ( a ) ihm and ( b ) pls model for the four - monomer copolymerization . 
 the predicted values were obtained by raman spectroscopy , and the 
 measured values were obtained by offline gc analysis . in comparison with an ih model , prediction of the 
 overall conversion 
 is better served with the pls calibration model . although ihm is a 
 powerful technique for predicting conversion , it appears to be unsuitable 
 for this specific system with significant spectral overlap . the pls model does not rely on a mechanistic 
 description of the spectra and allows one to achieve better predictions 
 of monomer concentrations despite low signal - to - noise ratios . the 
 observed decrease in intensity of the overall spectra in the 
 early stages of the polymerization reaction is associated with some 
 physical changes in the reaction mixture and might allow for a correlation 
 with particle size by either direct or indirect methods . possible 
 mechanisms behind the intensity suppression are turbidity , refractive 
 index , and increasing scattering due to the formation and growth of 
 particles . the latter possibility is the basis for an examination 
 of whether a single raman immersion probe could be used to monitor 
 both the concentration of monomers and the particle size of the product 
 polymer . several pls models 
 were developed using different spectral ranges and different spectral 
 corrections . the first model ( model 8) included the range of 150400 
 cm and correction of the baseline with a linear - fit 
 subtraction . for model 9 , the same spectral range ( 150400 
 cm ) was taken into account , but this time the 
 spectra were normalized to the band at 1000 cm . the differences between these models were 
 that model 10 corrected the baseline with a linear - fit subtraction 
 and model 11 also used normalized spectra . figure 6 shows the particle size in 
 an emulsion copolymerization reaction predicted by all four models 
 and the corresponding offline dls measurements . taking the entire untreated 
 spectrum into account ( 1501800 cm ) , model 
 10 gave a significant error in particle size prediction ( r = 0.68 ) . using the normalized spectra for the calibration , 
 model 11 gave a slightly higher error ( r = 0.66 ) . the reason for this is that the effect of growth in particle 
 size is partially filtered out by normalization . in both cases , the 
 pls model had rank 4 , which indicates the complexity of the model , 
 but was not too high to overestimate the correlation between the particle 
 size and raman spectra . ( b , d , f ) predictions of average particle size 
 using different pls 
 models compared with offline dls measurements for different experiments . ( a , c , e ) changes in raman intensity at low wavelength corresponding 
 to the performed experiments . experiments corresponding to graphs a , b and c , d were performed 
 at 60 c , and experiment corresponding to graphs e , f was performed 
 at 80 c . it is known that , at 
 low wavenumbers , vibrations of elastic spheres 
 and chain - expansion vibrations can be observed . therefore , pls models were built focusing on this region 
 ( 150400 cm ) . as expected , the pls models 
 for both the treated ( model 9 ) and untreated ( model 8) spectra exhibited 
 much better results than the models that included the entire spectral 
 range ( table 3 ) . it can be seen that , at the start of the reaction , 
 the models struggled 
 to estimate particle size . this is not surprising guven that , at the 
 beginning of a reaction , the emulsion solution consists of monomer 
 droplets , surfactant , and water but no polymer particles . the standard 
 dls instrument used in this study is capable of measuring particle 
 sizes in the range from 0.3 nm to 10 m . the beginning of the 
 reaction ( t = 0 ) was defined as zero particles ( d = 0 ) for the raman calibration set . however , figure 6 shows that , although 
 the models were trained for zero particles , the models misinterpreted 
 the scattering that occurred prior to nucleation . the discrete behavior 
 of emulsion polymerization might cause problems for a statistical 
 model , such as rapid changes in the number of particles at the beginning 
 of the polymerization followed by much slower growth of the particles , 
 which appears to be predicted rather well . the rapid changes within 
 the polymerization reactor at the start of the reaction give rise 
 to multiple scattering phenomena , which introduce errors in the linear 
 regression model . validation of the calibration models does show high 
 error for the prediction of zero particles ( supporting information , figure s14 ) . nevertheless , a pls model can 
 be used as a fast and reasonably 
 accurate method of monitoring particle sizes during emulsion polymerization 
 within the validity of the pls model calibration set . because the 
 pls models were also more accurate in predicting monomer concentrations , 
 a single type of spectral model with two different calibration sets 
 can be used to simultaneously measure monomer concentration and particle 
 size . predictions of particle size 
 with raman spectroscopy would be even more robust and accurate if 
 scattering could be described with a physical model . as known from 
 the literature , at low wavenumbers , acoustic vibrations of elastic 
 spheres can be observed . the frequency 
 shift of these vibrations depends on the size of the elastic spherical 
 particle . the possibility of observing such frequency shifts in raman 
 spectroscopy is well - established , and phonon - confinement or elastic - sphere 
 models are used to determine particle size . it has also been stated that , in the low - wavenumber 
 region ( < 400 cm ) , chain - expansion vibrations 
 can be observed . these are bending vibrations 
 in which all c  c  c angles are changed in phase , resulting 
 in the overall expansion and contraction of the aliphatic backbone . simulations of raman vibrations for styrene oligomers ( see supporting information ) have shown that chain - extension 
 vibrations are in the range of 200400 cm , that is , in the range observable with a typical spectrometer . this 
 might be the phenomenon that gives rise to the observed variations 
 in the spectra in this work ( see figures 68 ) . however , 
 at this stage , we have not developed a physical model linking chain - extension 
 vibrations to particle size . the changes in raman spectra occurring 
 during a polymerization 
 reaction involve not only changes in intensity , as discussed above 
 and used in statistical pls models , but also shifts in the peak position 
 at low wavenumbers ( see figure 7 ) . plotting the raman shift against the reaction time and 
 overlaying this plot with the change in particle size reveals a trend . 
 with increasing particle size , the raman intensity shifts to lower 
 wavenumbers . after a reaction time of about 20 min , the chain - extension 
 vibration does not change much , and its peak scatters at about 236 
  2 cm . this corresponds to the observed 
 conversion profile : at high conversions , the mean particle size no 
 longer changes significantly . comparison of offline measured particle size 
 ( red ) and peak shift 
 ( black ) during different experiments performed with the two - monomer 
 system . st / ba monomer ratios of ( a ) 80:20 at 80 c , ( b ) 50:50 
 at 60 c , ( c ) 50:50 at 60 c , and ( d ) 80:20 at 70 c . we observed experimentally the 
 shift in position of raman bands 
 as a function of time , or reaction progress , during emulsion copolymerization ( figure 8) . looking for 
 theoretical foundations for the shift in raman peak intensity , we 
 considered two simple models , namely , the elastic - sphere model and 
 surface - tension model , to calculate the vibrations of a spherical 
 particle that could give rise to a raman shift . variations in raman shift 
 as a function of reaction time . the equation for the frequency ,  , of an elastic sphere 
 was 
 derived elsewhere as1with 02 = /(0r ) , where  and 0 are 
 the shear modulus and bulk density , respectively . equation 1 has been found to provide 
 good experimental agreement for spherical clusters with particle diameters 
 of r  1020 nm irradiated by infrared 
 laser light with a wavelength   500 nm . the equation was derived from a continuum approach 
 applied to the problem of normal elastic vibrations of a macroscopically 
 small spherical particle . equation 1 can not be used for monopole excitation ( l = 0 ) because the assumption of negligible fluctuations in density 
 was considered . the dipole field ( l = 1 ) of poloidal 
 displacements contributes only to the parameter of inertia , whereas 
 the restoring force ( the parameter of stiffness ) of the vibration 
 is canceled . therefore , the lowest multipole degree of a spheroidal 
 mode is the quadrupole ( l = 2 ) . considering 
 only quadrupolar vibrations ( l = 2 ) 
 of polystyrene particles with  = 3  10 kg 
 m s ,  = 1040 kg m , and r = 50  10 m , the frequency is given by2yielding3to calculate the wavenumber , we assumed that 
 the phase velocity was equal to the speed of light in vacuum and that 
 the wavenumber was equal to4thus , a polystyrene sphere of 100-nm diameter 
 will vibrate at k = 23 cm . this 
 vibration is too low to be detected by our raman spectrometer because 
 of overlap with the rayleigh wing . the instrument used in the present 
 study can measure raman shifts of at least 50 cm . the experimentally observed shifts are in the range of 200250 
 cm and can not be explained by the vibrations of 
 a sphere in the quadrupolar state . to test whether the observed 
 peak shift to lower wavenumber can 
 be explained by the elastic sphere model , we calculated raman shifts 
 as a function of particle size using the elastic sphere model ( table 3 ) . the sphere model predicts a vibrational shift to 
 lower wavenumbers with increasing particle size . however , the ranges of the vibrations were 
 rather different between the model and experiment . lamb proposed that the 
 frequency of a resonant mode of shape oscillation for a free inviscid 
 liquid droplet in air with axial symmetry can be expressed as5where  is the frequency , l is the mode number / resonant 
 mode ,  is the density , r is the equilibrium 
 radius , and  is the surface 
 tension . although eq 5 considers a free inviscid liquid droplet in air , the equation can 
 be applied to our system for a rough estimation of the region where 
 the particle vibration should be . the resonant mode is l = 2 , which is , as mentioned earlier , a raman - active mode . other 
 values for the calculation are the density (  = 1040 kg m ) , particle size ( r = 50 nm ) , and 
 surface tension (  = 10 mn m ) . the 
 result for the frequency using the given values is6to obtain the wavenumber k , the frequency should 
 be divided by the speed of light , giving7the estimated range for the vibration 
 of a 
 spherical particle is too close to the laser line to be detected by 
 most raman spectrometers . thus , to date , we can not accurately correlate 
 the observed shift in raman spectra at 240 cm with 
 a specific chain - expansion mode and particle size . nor can we find 
 another fundamental scattering mechanism to predict raman shifts as 
 a function of particle size . in 
 this work , we have shown the possibility of increasing the observability 
 in a batch copolymerization process by employing a fiber - optic immersion 
 raman probe . we have shown that this technique can be used for monitoring 
 the conversions of individual monomers in reasonably complex comonomer 
 systems , or at least the overall conversion , using statistical pls 
 calibration models . it is also feasible to develop a pls model for 
 monitoring particle sizes using the low - wavenumber spectral range . this shows the feasibility of monitoring both conversion and particle 
 size using a single physical probe . there remain limitations for spectroscopic 
 techniques in the case of low concentrations of monomers and complex 
 monomer mixtures . we have identified that the observed shift 
 in raman spectra in 
 the range of 200250 cm correlates with 
 the chain expansion vibration . however , we were unable to find a first - principles 
 model to correlate the particle size with the observed raman shifts
an 
 immersion raman probe was used in emulsion copolymerization 
 reactions to measure monomer concentrations and particle sizes . 
 quantitative 
 determination of monomer concentrations is feasible in two - monomer 
 copolymerizations , but only the overall conversion could be measured 
 by raman spectroscopy in a four - monomer copolymerization . 
 the feasibility 
 of measuring monomer conversion and particle size was established 
 using partial least - squares ( pls ) calibration models . a simplified 
 theoretical framework for the measurement of particle sizes based 
 on photon scattering 
 is presented , based on the elastic - sphere - vibration 
 and surface - tension models .