Joseph L Polman

Roy D Pea

Transformative Communication in Project Science Learning Discourse

How can teachers help their students learn ideas and strategies that are almost completely foreign to the students' experiences? This problem is faced daily by teachers who are trying to help their students learn complex subject matter and tasks such as scientific or historical inquiry. Traditional wisdom would have the teachers simply tell their students what they need to know. However, constructivist theory and research, including Piagetian, information-processing, and social constructivist approaches, has done much to emphasize that telling students is not enough to ensure that they have learned something. Instead, the students must construct their own knowledge, perhaps with the teachers' help. Say a teacher is trying to help students learn how to use data from an analysis as evidence to support a claim in scientific inquiry, in a way that seems much different from anything the students have been challenged to do in the past. Popular wisdom, rooted in the work of Dewey (e.g., 1902), would have the teacher ask the students to "learn by doing" within the context of a science research project. Still, if students lack a preexisting foundation of knowledge and experience that can be easily related to the science research project, the teacher's invitation to "do a project" will fall on uncomprehending ears. How can students build this new knowledge when there is seemingly no foundation and few raw materials in their mental toolkit with which to build the desired cognitive structures?

, the commonly held view that knowledge is actively con-

P A G E P R O O F S

structed by learners encounters a paradox at a fundamental level. How learners can process information so as to construct new cognitive structures that are more complex than their already existing cognitive structures is unclear. As [START_REF] P A G E P R O O F S Fodor | Fixation of belief and concept acquisition[END_REF]

forcefully put it:

There literally isn't such a thing as the notion of learning a conceptual system richer than the one that one already has; we simply have no idea of what it would be like to get from a conceptually impoverished to a conceptually richer system by anything like a process of learning. (p. 149, cited in Bereiter, 1985) In this chapter, we argue that a solution to the learning paradox as well as teachers' everyday dilemmas lies in a neo-Vygotskian theory of distributed intelligence and transformative communication. After laying out the theoretical background, we illustrate the use of a specific discourse strategy for transformative communication that has proven particularly useful in teaching-learning situations such as project-based science.

DISTRIBUTED INTELLIGENCE AND THE LEARNING PARADOX

In previous works, Pea (1993b[START_REF] Pea | Learning science through collaborative visualization over the Internet[END_REF] has argued that intelligence is more realistically conceived as distributed among persons and the symbolic and physical environment rather than within individual, isolated minds. In addition, intelligence is more aptly viewed as manifest in the dynamics of activity, rather than as static. The distribution of intelligence among persons is often evident in collaborative activity (e.g., [START_REF] Barron | When smart groups fail[END_REF][START_REF] Roschelle | Learning by collaborating: Convergent conceptual change[END_REF] and dialogue in parent-child dyads (e.g., [START_REF] Rogoff | Apprenticeship in thinking: Cognitive development in social context[END_REF]-in many such instances no individual can be said to be the one who has solved a problem or accomplished an activity. One of the most evident examples of this co-constructive activity lies in early language development-the transitional time following the single-word utterance period, and before the regular use of syntactic, multiword utterances, is marked by the collaborative development of full sentences, over speaker turns and across speakers [START_REF] Ochs | Propositions across utterances and speakers[END_REF]. Consider an example described by [START_REF] Wertsch | Voices of the mind: A sociocultural approach to mediated action[END_REF]: A child has lost a toy, and she approaches her father for help. The father does not know where the toy is but asks the child a series of questions that help her structure her search. Did she have it in her room? No. In the yard? No. In the car? That could be. They check and find the toy in the car. It is the child-parent system that solved the problem, with unique contributions from both persons that the other did not supply. Numerous researchers and theorists following in the footsteps of Russian sociocultural research (e.g., [START_REF] Leont'ev | The problem of activity in psychology[END_REF][START_REF] Vygotsky | Mind in society[END_REF] have been refining the vision of intelligent action carried out between persons, in what [START_REF] Wertsch | Voices of the mind: A sociocultural approach to mediated action[END_REF] terms the intermental realm.

As Pea has recounted in more detail elsewhere (1993b), he was struck by the fact that although many were recognizing the distribution of intelligence across persons, the contribution of designed objects such as physical tools, computer programs, or inscriptional systems such as x-y coordinate graphing to intelligent action was often neglected. [START_REF] Vygotsky | Mind in society[END_REF] had emphasized the importance of cultural tools in mediating human action, but he had focused on language as a tool. Ironically, given the concreteness of the "tool" metaphor, concrete physical P A G E P R O O F S tools and nonverbal but semantically rich representational systems had often been neglected in analyses of distributed cognitive activity. But the integral use of artifacts such as pencils and lists in everyday cognitive achievements highlights the ubiquity of tools in our surroundings, which have certain sorts of intelligence "built in." Some of our work has focused on how educational designers can build in more effective affordances for cognitive tools such as software designed to support science inquiry (e.g., [START_REF] Edelson | Addressing the challenges of inquirybased learning through technology and curriculum design[END_REF][START_REF] Gordin | The Climate Visualizer: Sense-making through scientific visualization[END_REF]Pea, 1993aPea, , 1998) ) in the geosciences.

In this chapter, and other recent work, we are more directly concerned with the ways in which intelligence is distributed in social arrangements and activity structures that support human learning through "guided participation" (Polman, 2000, in press; [START_REF] Polman | Transformative communication as a cultural tool for guiding inquiry science[END_REF][START_REF] Rogoff | Apprenticeship in thinking: Cognitive development in social context[END_REF]. Examples of such arrangements include [START_REF] Palincsar | Reciprocal teaching of comprehension-fostering and comprehension monitoring activities[END_REF] influential model of "reciprocal teaching," in which the teacher places students in roles that divide important aspects of the reading task, supports the accomplishment of those roles, and through repeated activity involving role shifts for students brings the group as a whole to more expert performance.

Strategies such as reciprocal teaching are based on [START_REF] Vygotsky | Mind in society[END_REF] "general genetic law of cultural development." Vygotsky held that learners accomplish activities with the help of more expert others in a social setting-on the intermental [START_REF] Wertsch | Voices of the mind: A sociocultural approach to mediated action[END_REF] plane between minds-that the learners could not achieve on their own. This sort of intermental action is for the individual learner what Courtney [START_REF] Cazden | Performance before competence: Assistance to child discourse in the zone of proximal development[END_REF] aptly calls "performance before competence." After such performance, learners can advance their own understanding, on what Wertsch terms the intramental plane (i.e., within an individual's mind). The student-and-teacher-acting-together-in-the-world thus provides a structure, which the student can then internalize so that the student can later act in a similar fashion without the teacher's help [START_REF] Cole | Cultural psychology: A once and future discipline[END_REF]. Related considerations apply to the conditions under which an individual may elect to use external representations or tools in the environment to serve as scaffolds of their own activity, because of the stressful demands of the task situation-"internalization" is thus not a trait that an individual develops for a task but a state of the situation (Pea, 2004; also see [START_REF] Glick | Toward a holistic developmental psychology[END_REF], as when an adult uses "egocentric speech" to help plan a complex activity in a noisy situation.

This would seem to provide a solution to the learning paradox: the building blocks for new conceptual structures are not just an individual's concepts in the head but also the sociocultural world and actions in it that can be internalized. As [START_REF] Bereiter | Toward a solution of the learning paradox[END_REF] has pointed out, however, there is a catch in the use of the term internalized, which Vygotsky's research group also recognized. If the more complex cognitive structures end up being completely "in the head," then their building blocks must also be located there. To some degree, this problem is mitigated by the idea that the memories of action sequences carried out with the support of others could serve as the building blocks themselves, provided the actions are designed in such a way as to scaffold for future "fading" of support (for an example with reading strategies, see Cole, 1996, pp. 272-280). Researchers rooted in the tradition of computational cognitive modeling of individual minds have been exploring this sort of learning for some time, under the rubric of case-based reasoning (e.g., [START_REF] Kolodner | Promoting transfer through case-based reasoning: Rituals and practices in Learning by Design™ Classrooms[END_REF][START_REF] Schank | Tell me a story: A new look at real and artificial memory[END_REF]; they have developed informa-

P A G E P R O O F S

tion-processing paradigms whereby the memories of event sequences can be stored, retrieved, and adapted in reasoning about possible future actions.

Regardless of the adequacy of such approaches, we would join others in emphasizing that not all forms of distributed intelligence can reasonably be described as eventually or ideally "internalized" (e.g., [START_REF] Hutchins | Learning to navigate[END_REF][START_REF] Hutchins | Cognition in the wild[END_REF]Pea, 1993bPea, , 2004;;Wertsch, 1997). To take Hutchins's oft-cited example, the idea that the navigation of a large naval vessel is or should be meaningfully located in one individual's head verges on nonsensical: The carrying out of navigation is always and always should be embedded within a distributed social and material-technical system. In the social realm, many persons playing complementary roles are necessary, and in the material realm, a great deal of specialized equipment with embedded intelligence of various sorts is necessary. Exploitation in the real-time achievement of intelligent activity is also required.

Due to consideration of cases such as navigation, and the ongoing importance of context and tools for much intelligent action, many researchers have come to prefer terms such as appropriation [START_REF] Brown | Distributed expertise in the classroom[END_REF][START_REF] Pea | Augmenting the discourse of learning with computer-based learning environments[END_REF][START_REF] Rogoff | Apprenticeship in thinking: Cognitive development in social context[END_REF] and/or mastery [START_REF] Wertsch | Mind as action[END_REF] rather than internalization. Unlike internalization, the terms appropriation and mastery do not imply that residuals "in the head" are unsupported by tools in the world. Some sort of mental representations are appropriated by individuals intramentally and can be applied across multiple contexts, but the mental representations do not do the work of cognition alone. Because much of the complexity of cognitive achievements always remains in the cultural and material world, the learning paradox is not necessarily a problem. There are continually dialectical processes in which the "internal uses" of cognitive structure are complemented by the affordances of external tools, representations and features of the physical as well as social environments in which the learner operates. The tools that an individual needs to carry out actions may not be available in all settings, but part of what humans do is create or arrange their environments so that not all the work to be done requires mental gymnastics (Pea, 1993b). Further, it is important to note that the individual mental representation involved in mastery of a tool does not require a full description of a tool's complexity. In other words, the understanding of how tools work is not necessary for their mastery. For example, we do not have to understand how our computers work at the electronics level or even the programming level to use our word processors in an expert way. Recalling [START_REF] Cazden | Performance before competence: Assistance to child discourse in the zone of proximal development[END_REF] phrase "performance before competence," we are emphasizing that "competence" does not always imply complete understanding of all aspects of the performance; rather, the person's contribution to intelligent action must "dovetail" [START_REF] Clark | Being there: Putting brain, body, and world together again[END_REF] with the tool's affordances. Dovetailing effectively with tools in the world does not require that we have complete copies of tools and how they work in our heads [START_REF] Clark | Being there: Putting brain, body, and world together again[END_REF]. We may have to understand a good deal of how the computer and software works to invent the word processor from scratch, but as James Burkes's Connections series remind us, even inventions often involve the combination of existing ideas and devices in new ways, with or without an understanding of the parts' origins and operation. The re-usability of intelligent tools designed for certain purposes is the great insight of object-oriented programming: Code that performs certain operations does not have to constantly be reinvented but instead can be invoked from within multiple contexts.

P A G E P R O O F S

TRANSFORMATIVE COMMUNICATION IN GUIDED PARTICIPATION

Although the learning paradox may not be a philosophical problem given this neo-Vygotskian viewpoint, how to support learners so that they can appropriate some valued aspects of activity is a constant dilemma for teachers. In [START_REF] Vygotsky | Mind in society[END_REF] terminology, the zone of proximal development (ZPD) describes the limit of actions that learners can meaningfully participate in intermentally, and subsequently appropriate intramentally. Beyond the ZPD, learners cannot relate actions to their current understandings. How teachers and students can accomplish learning and activity in the ZPD is not at all straightforward. To be most effective, teachers must diagnose where students are developmentally and figure out, in each case, what it would look like for the students to perform meaningfully, if not yet fully competently. For teachers, like experts in a domain, it may be quite difficult to avoid inadvertently acting outside a novice's ZPD. In our work within the CoVis project (Pea, 1993a), we were faced with these issues in a realm where students appeared to be facing somewhat of a "bootstrapping" dilemma: They had few experiences that helped them to know how to carry out certain aspects of science inquiry, much less use the Internet and scientific visualization tools in the context of that higher-order activity [START_REF] Polman | Bootstrapping a community of practice: Learning science by doing projects in a high school classroom[END_REF]. Thus, if the teacher just gives them a clearly circumscribed path, as is done in many traditional labs, the meaning of the actions students carry out will not necessarily relate to the teacher's goal of students learning about experimental design (because the students are not required to participate in the design). This problem is also too often manifest in various forms of student-scientist partnerships in education [START_REF] Cohen | Internet links for science education: Student-scientist partnerships[END_REF]. In studies such as the multinational precollege GLOBE Project (Global Learning through Observations to Benefit the Environment), students collect data around the world. They do so according to protocols that are designed by scientists to ensure data quality and reliability, and without care, in designs such as these, learners may be relegated to the role of "databots," collecting data without an understanding of the designs that render the data meaningful [START_REF] Pea | Science education as a driver of cyberspace technology development[END_REF]. Teachers cannot just give the students the steps to follow by rote, nor can they leave the students unguided to recapitulate the development of all science knowledge. What is needed is some kind of interactive process of guided participation, which allows the student to be an active inquirer and the teacher to be an active guide. "Transformative communication" is one such process for guiding participation [START_REF] Pea | Seeing what we build together: Distributed multimedia learning environments for transformative communications[END_REF]; we came to see that it provides some explanation of why certain incidents prove productive for teaching and learning in a project-based science classroom.

The view of communication as transformative can be contrasted with common views of communication as ritual and as transmission [START_REF] Pea | Seeing what we build together: Distributed multimedia learning environments for transformative communications[END_REF]. The view of communication as ritual tends to encourage active participation by all parties, but in activities with already shared meanings. The ritual nature of much cultural activity helps to explain how it is successfully carried out: for instance, telephone greetings rely on a highly specific series of key words, pauses, and intonations to get a great deal of information across quickly [START_REF] Schegloff | Identification and recognition in telephone conversation openings[END_REF]. Despite the obvious importance of ritual communication in cultural activity, it does not involve the sort of generativity at fostering new development that is needed for education.

P A G E P R O O F S

The dominant view of communication in learning settings as transmission of knowledge from the teacher to the student [START_REF] Cohen | Teaching practice: Plus ça change[END_REF][START_REF] Pea | Seeing what we build together: Distributed multimedia learning environments for transformative communications[END_REF][START_REF] Polman | Designing project-based science: Connecting learners through guided inquiry[END_REF] is associated with entirely teacher-directed pedagogy such as lectures [START_REF] Rogoff | Developing understanding of the idea of communities of learners[END_REF]. In lecture-based classrooms, the teacher is an active presenter of knowledge and the students are passive receivers of knowledge. In part because of the recognition already discussed that knowledge is actively constructed (e.g., [START_REF] Bransford | How people learn: Brain, mind, experience, and school[END_REF], educational reform efforts such as project-based learning are often designed in hopes of changing the students' passivity. When implemented as unguided discovery, however, project-based learning demands that students become active in the acquisition of knowledge, but it leaves teachers passive. Rather than either of these extremes, educational researchers have come to recommend the model of "community of learners," in which "learning occurs as people participate in shared endeavors with others, with all playing active but asymmetrical roles" (Rogoff, 1994, p. 209; see also [START_REF] Brown | Guided discovery in a community of learners[END_REF]. Teachers interested in supporting inquiry learning, rather than just "letting their students go" to see if learning will occur, would thus do well to try to create a "community of learners" atmosphere in their classes. This implies that they must play a unique role of structuring and guiding student activities without taking away the students' active role. Some researchers refer to this middle ground as "guided discovery" or "guided learning," but note that the role of guide is difficult to master. Ann [START_REF] Brown | Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings[END_REF] notes, Guided learning is easier to talk about than do. It takes clinical judgment to know when to intervene. Successful teachers must engage continually in on-line diagnosis of student understanding. They must be sensitive to overlapping zones of proximal development, where students are ripe for new learning. Guided discovery places a great deal of responsibility in the hands of teachers, who must model, foster, and guide the "discovery" process into forms of disciplined inquiry that would not be reached without expert guidance. (p. 169) As Brown points out, the complexity of structuring and guiding students in project work is increased because different students in a class need different levels and kinds of support; because their existing knowledge bases are different, the individuals in a class end up interpreting whatever support they get, even if it is a statement by a teacher to the whole class, differently as well. Matching the kind and level of support students need with what a teacher provides them is a difficult balance to maintain, though. Consequently, as one teacher put it, a teacher trying to support students can "feel sort of like a tree swaying between two extremes of providing students with structure and allowing them to do it all themselves." One way to conceptualize teachers' new role in such classrooms is by scaffolding student work [START_REF] Collins | Cognitive apprenticeship: Teaching the craft of reading, writing, and mathematics[END_REF]. Scaffolding can occur either by modeling, by structuring activity, or by coaching-supporting and guiding students' work along the way. In this chapter, we are most concerned with the use of one powerful form of coaching, transformative communication, in a project-based science class. So what is transformative communication? [START_REF] Pea | Seeing what we build together: Distributed multimedia learning environments for transformative communications[END_REF] has described it as follows:

The initiate in new ways of thinking and knowing in education and learning practices is transformed by the process of communication with the cultural messages of others, but so, too, is the other (whether teacher or peer) in what is learned about the unique Transformative communication is achieved through mutual appropriation [START_REF] Newman | Social constraints in laboratory and classroom tasks[END_REF]Pea, 1993b) by participants in social interaction to create meanings that neither participant alone brought to the interaction. In some project-based science classrooms-ones designed to support students in carrying out their own original research-it involves transforming students' actions into more successful "moves" in the "language game" of science [START_REF] Wittgenstein | Philosophical investigations[END_REF]. Put another way, it allows students to participate in a new way in "talking science" [START_REF] Lemke | Talking science: Language, learning, and values[END_REF][START_REF] Pea | Augmenting the discourse of learning with computer-based learning environments[END_REF].

GETTING TO SPECIFICS: METHODS, DATA SOURCES, AND FRAMEWORKS

All this discussion will only be meaningful insofar as it can be related to specific learning environments and conversations. For the balance of this chapter, we discuss episodes involving transformative communication in one classroom.

The episodes related in this chapter are part of a larger interpretive case study [START_REF] Polman | Designing project-based science: Connecting learners through guided inquiry[END_REF] conducted from 1994 through 1996 in Rory Wagner's 1 class, one of many participating in the CoVis Project. One of the central features of the class was that students conduct Earth Science projects of their own design. What this meant in practice is that they participated in the formulation of a research question, the gathering of data to provide empirical evidence for addressing the question, analysis of those data, and reporting in both written and oral formats.

Polman was a participant observer in Wagner's classroom for 3 years-1½ years acting as a technical assistant and 1½ years conducting the formal study (1994-1995 through winter 1995-1996). Data were collected in field notes and videotapes of classroom observation at each project phase, artifacts created by the teacher and students, and formal and informal interviews with the teacher and selected students. Formal interviews were recorded with audiotape and transcribed, whereas informal interviews were recorded with handwritten notes. For this chapter, we use to illustrate ways transformative communication was used in specific episodes to scaffold students' accomplishment of science inquiry.

Our interest in these episodes began with a vague recognition that they seemed to involve some sort of "ah ha" quality among participants and played a key role in the subsequent success of the projects of which they were a part. We thought that a better understanding of the episodes might enable researchers and teachers involved in our project to foster more widespread success, for the challenges of project-based science learning are many. We came to recognize that part of the power of the episodes was due to the fact that they involved mutual appropriation and transformative communication. We surmised that an adequate description of what was unique about them could provide elements of a prescription for future effective action. Table 12.1 provides our general description of the episodes in the form of a dialogue sequence that transformative communication followed.

We do not intend to imply that all communication that results in learning is transformative in the manner described here. Nor do we mean to imply that all communication that could reasonably be termed transformative follows this sequence in strict stepwise order; the sequence is intended to describe the general

P A G E P R O O F S
trajectory of some key dialogues, which inevitably involve a great deal of interactive give-and-take that we are not going to examine at the level of detail afforded by, for instance, conversation analysis (as in Polman, in press). What we hope to accomplish with analyzing this dialogue sequence is twofold: (1) to describe important features of dialogue that have proved productive in transformative teaching-learning episodes, and (2) to provide a discourse strategy that teachers may productively use as a cultural tool in future episodes with their students. In summarizing these cases, we focus on how student groups conducting projects arrived at an incident of transformative communication, their interaction with the teacher going through the steps of the dialogue sequence, and the subsequent impact of the transformative communication event on the progress of their project.

PLESIOSAURS: TRANSFORMING A QUEST FOR "THE FACTS" INTO A RESEARCH QUESTION

As detailed elsewhere (Polman, 2000, in press), Wagner guided his students through open-ended projects through a project unit activity structure [START_REF] Doyle | Classroom tasks and students' abilities[END_REF][START_REF] Lemke | Talking science: Language, learning, and values[END_REF][START_REF] Mehan | Structuring school structure[END_REF] consisting of several parts, each leading to the next, with "milestone" deliverable artifacts due from the students at many of them. The complete series of milestones was (1) select group and topic, (2) write up background information, (3) provide research question/proposal, (4) collect data, (5) analyze data, (6) complete research report modeled on the scientific research article genre, (7) revise research report, and (8) present to the class. Somewhat akin to inscriptions made by professional scientists [START_REF] Latour | Drawing things together[END_REF][START_REF] Gordin | The Climate Visualizer: Sense-making through scientific visualization[END_REF], the written milestone artifacts are "shared, critiquable externalizations of student knowledge" [START_REF] Blumenfeld | Motivating project-based learning: Sustaining the doing, supporting the learning[END_REF][START_REF] Guzdial | Artifacts of learning: A perspective on students' learning processes and strategies through their learning products[END_REF] that become useful as occasions for feedback and transformative communication. Three 11th-grade young women named Beth, Laura, and Cindy teamed up for their first project in Wagner's class. Beth emerged as their leader, with Laura making frequent contributions and Cindy mostly remaining quiet in the background. Cindy and Laura decided one day when Beth was not present that their project Students make a move in the research process with certain intentions, guided as well as limited by their current knowledge.

(2)

The teacher does not expect the students' move, given a sense of their competencies, but understands how the move, if pursued, can have additional implications in the research process that the students may not have intended.

(3)

The teacher reinterprets the students' move, and together students and teacher reach mutual insights about the students' research project through questions, suggestions, and/or reference to artifacts.

(4)

The meaning of the original action is transformed, and learning takes place in the students' zone of proximal development, as the teacher's interpretation and reappraisal (i.e., appropriation) of the students' move is taken up by the student.

topic should be an extinct sea creature called a "plesiosaur." Part of the creature's appeal was its long neck, somewhat like that of a brontosaurus, which made it look in artists' renderings like the fabled Loch Ness monster. Beth, Laura, and Cindy initially had a great deal of trouble locating any specific details on the plesiosaur for the "background information" phase, but with Wagner's assistance they located World Wide Web resources related to the creature. They used the information from the Web and library books to write up their background information report. During the following week, the Plesiosaur group had to complete their focused research proposal. After a whole-class, teacher-led discussion on research questions, students began working in their groups generating potential questions about their topics. The next day, Beth and Cindy approached Wagner to announce they had a research question: "Are accumulations of plesiosaurs associated with areas of high marine productivity?" Wagner was pleased that they followed his advice on choosing a question examinable with empirical data, but he feared the spotty plesiosaur fossil record would prevent the students from coming to valid conclusions about locations in which they thrived; in essence, some locations where plesiosaurs dwelled might have been conducive to fossil formation and discovery, and others not, leading to spurious trends. To avoid these pitfalls, Wagner asked them to reconsider what attracted them to plesiosaurs as a topic in the first place. In response, Cindy mentioned their long necks, and Beth how they swam with large flippers. That reminded Wagner of a comment Beth had made while looking at library books 2 weeks earlier. She had announced, "This [book] says they flew through the water like sea turtles, and sea turtles swim very quickly … This [book] says they didn't swim very quickly." Wagner had not followed up on the comment at the time, perhaps because he was interrupted by a question from another student. The group had not mentioned swimming speed in their background information milestone report, but the teacher recalled it. Referring to these books, he asked, "Didn't you read a debate about whether [plesiosaurs] were fast or slow swimmers?" Beth confirmed, "Some of them said they were fast and some said slow."

In this exchange, it is notable that Wagner interpreted and recalled the conflicting accounts of plesiosaur swimming speed as a scientific debate, which he understood in terms of the scientific community of scholars attempting to reach consensus. The student, on the other hand, had simply noted that the accounts related different ideas but did not understand those ideas within the frame of "scientific debate." Based on his assumption that there was a debate about swimming motion, Wagner suggested they could do an "analysis of swimming motion … like how fast they go. You would need to know how animals move and how they swim." Thus, Wagner "revoiced" (O'Connor & Michaels, 1996) the information Beth had originally stated, with a reconceptualization [START_REF] Cazden | Classroom discourse: The language of teaching and learning (2nd Edition)[END_REF] to include the notion of scientific debate. Beth and the other members of her group liked the idea and decided to run with it. As Beth said, it reminded her "of the reanalysis of dinosaurs that they did and whether they were slow or fast-Jurassic Park was more accurate than the old picture of lumbering dinosaurs." With this reference to a popular culture notion that helped her understand scientific debates about the speed of extinct creatures, Beth began to better understand the process of science inquiry.

Following this discussion, during which they decided to focus on the swimming motion of plesiosaurs, the group members reviewed the relevant sections in

P A G E P R O O F S

the library books they had gathered, and Beth returned a few days later saying incredulously, "Mr. Wagner! Do you know whether the plesiosaur moved by rowing its flippers or flapping them like wings?" One of her library books reported that Plesiosaurs swam with a rowing motion, and another book mentioned that they swam by underwater flight, flapping their flippers like wings straight up and down in the water. Again, neither book mentioned a controversy. As Beth reported later, she "thought he was like all-knowing." She appeared to be looking for her teacher to provide the answer, the kind needed for what he called "traditional library research." Wagner was determined to have her do more extensive inquiry, however. Beth, by her own admission, "had never done a project where there [wasn't] really an answer, or someone who's already found the answer." Wagner showed Beth that her question about the swimming method could be more than a quest for the accepted fact; it could be their research question-they could assemble evidence to support their own claim of how plesiosaurs swam.

This interaction enabled Wagner to support Beth in accomplishing an activity with which she was unfamiliar, by means of the sort of "transformative communication" described earlier. We can see a concrete enactment of the 4-stage dialogue sequence shown in Table 12.1: (1) Beth approached her teacher looking for the answer to two fact-based questions that she expected her "all-knowing" teacher to provide: Did plesiosaurs swim fast or slow, and did they swim by "underwater flight" or a rowing motion? If she could get the answers, she would include them in her report on plesiosaurs, which she may have been seeing still as a library research project like she had done in other classes, with established facts about a topic synthesized and described. (2) Wagner did not know the fact Beth was looking for, nor was he sure there was a debate about plesiosaur swimming motion, but he did know that part of the game of science involves marshaling evidence to support one of several competing claims such as the ones in the books Beth had found. (3) The teacher reconceptualized Beth's move, admitting he did not know the answer but pointing out that an interesting project could use this as a research question. They talked about how she and the other group members could contribute new evidence to a scientific debate rather than just report others' findings. (4) Beth's fact question has been transformed into a research question, as evidenced in her subsequent practice. The student group framed their data collection and analysis in terms of this debate and marshaled the evidence they could to support the theory of a slow rowing motion.

UFO SIGHTINGS: TRANSFORMING A CITATION INTO AN OPPORTUNITY FOR CONFIRMING RESEARCH

Researchers on tutoring and project-based learning have pointed out that motivational benefits can be reaped when students are given control over decisions about what they do-as Wagner gave Beth and her project partners-and when they are given the opportunity to work on problems and projects that interest them [START_REF] Blumenfeld | Motivating project-based learning: Sustaining the doing, supporting the learning[END_REF][START_REF] Lepper | Motivational techniques of expert human tutors: Lessons for the design of computer-based tutors[END_REF]. Bruce, Sylvia, and Cheryl's project shows how a project built on students' interests that might seem dubious at first from a scientific standpoint can be transformed into tractable empirical research. Through transformative communication, their project went from being a project about "whether UFOs are alien space ships" to a project about confirming or falsifying natural explanations of UFO sightings.

P A G E P R O O F S

Along with the other groups, the UFO Sightings group began their project by collecting and synthesizing background research on the topic, before deciding on a specific research question. In their interim report of background research, they mentioned the so-called Condon report [START_REF] Condon | Final report of the scientific study of unidentified flying objects[END_REF]), an official study put out by the U.S. government, in which UFO sightings were explained by meteor showers, rocket launches, and other known phenomena. Two days after he got the milestone background information reports from students, Wagner mentioned to Polman before class that Cheryl, Bruce, and Sylvia might need extra support on their project given the problematic nature of the UFO topic in the previous classes. He was pleased with the potential in the group's description of the Condon report, as the government's analysis took an empirical approach based on supportable or refutable claims about alternate explanations for UFO sightingsessentially taking a scientific approach to a problem usually approached through mere hearsay. So during class that day, Wagner initiated a discussion with the UFO Sightings group about potential research questions. The interaction with the UFO Sightings group proved a pivotal incident of transformative communication resulting in the formulation of a specific research question.

Shortly after completing attendance and answering some procedural questions from various students about the research proposal assignment, Wagner sat down with Cheryl, Bruce and Sylvia. The following interaction took place: That's another thing people do in science …

He described the example of the cold fusion debate a few years ago, pointing to how it could be applied in their project:

These guys said they had created cold fusion in the lab. But when other people tried it, they couldn't duplicate what they said ... In science, once someone says they've proved something, others check it … The idea [here] is to verify the government's explanations. Say they said it was a meteor shower. You could look at the date, where the meteor shower was, and when and where people saw the UFO. Does it match the same spot? If the sighting was here [points one direction] and the meteor shower there [points another direction], the government's explanation could be wrong.

The students decided to run with the idea. In this example, the students originally presented the Condon report as relevant to the history of the UFO debate and thus something to be cited in a review of literature but otherwise not used. Through their interaction, the teacher and students created a new meaning for the citation: the seeds of a study intended to provide independent confirmation or falsification. Thus, this sequence of interactions, starting with the submission of the report by the students and continuing with the discussion in class, can be seen as another instance of transformative communication. The students referred to some research in their background information report, intending it as an example of what is known and has been reported about their subject. Based on his greater understanding of the scientific process of verification, Wagner showed the students they could use the study as the seeds for the next phase of the activity structure: a research proposal to independently confirm or falsify the previous research.

After this interaction, the group's research formulation proved fruitful. For their final research report, the group chose four UFO sightings from the 1960s, described in the Condon report, and tried to independently confirm or falsify Condon and Gillmor's explanations. Their independent confirmation was based on printed data sources found in library searches, such as NASA launch records [START_REF] Stanford | NASA launch bulletin[END_REF]) that confirmed a scheduled re-entry of satellite Agena into the Earth's atmosphere occurred at the time an airplane crew reported a UFO over Mexico and could have been seen in that location.

Rory Wagner has found the "beginning of the project and the end of the project" to be the most difficult for students. Specifically, the early phase requires that students formulate a research question and proposal, and the later phase requires that they use data analysis to reach an empirically supported conclusion. The UFO Sightings project and the Plesiosaur project (described earlier) provide examples of transformative communication in the form of "action negotiation dialogues" (Polman, in press) around the formulation of research questions. The Hurricanes and the Moons projects provide examples of transformative communication at the data analysis phase.

HURRICANES: TRANSFORMING AN INTUITION INTO A CODING SCHEME

Dave and TJ became interested in hurricanes because of the destruction they cause. Through conversations with Wagner and a scientist "telementor" (O'Neill & [START_REF] O'neill | Why educate "little scientists?" Examining the potential of practice-based scientific literacy[END_REF][START_REF] O'neill | Mentoring in the open: A strategy for supporting human development in the knowledge society[END_REF] Wagner put them in contact with by e-mail, the students settled on the research question "Is there a preferred pattern of hurricane movement in the Northern Hemisphere?" Over the 2-week data collection period, TJ and Dave worked diligently to gather image data showing hurricane paths off a Web site they found linked from a page their telementor had directed them to. They began their data analysis by combining the hurricane paths onto one image, which gave them an impression of the shapes those paths could take. In an interview outside of class, Dave noted that many of the hurricanes made "a little semicircle" on the southeast edge of the United States.

P A G E P R O O F S

However, figuring out how to turn this general impression into an analysis of data supporting their conclusions proved difficult for Dave and TJ, as it did for most of their peers in Wagner's class. They turned in an initial stab at an analysis of 4 seemingly random years and got some advice from their teacher about choosing a larger sample of continuous years. With a day to go before their research report was due, Dave and TJ had a long conversation with Wagner trying to solidify data analysis techniques. Their teacher asked them what the general pattern of hurricanes was, and TJ showed him the semicircle or "C" shape Dave had described previously. Wagner made a few suggestions for ways to systematically describe many hurricane shapes, while they continued to look over the composite image of hurricane paths. Then Wagner noticed that not all the hurricanes followed the C-shaped path Dave and TJ had described. Some were straighter than the standard C, and others appeared erratic. He then suggested they could devise a categorization scheme for the shapes of paths. They could go back to each year and put a categorical label on each hurricane path shape, count up the frequencies of each shape, and calculate the percentages.

The conversation about data analysis was productive from Wagner's standpoint and nearly constituted a complete sequence of transformative communication. But because Dave and TJ did not effectively take up the jointly developed idea about categories of path shapes in the day remaining for the preparation of their written project report, it was not complete.

In his extensive commentaries written on Dave and TJ's report, Wagner tried to be encouraging and concretely helpful to move them forward. He wrote that they had "made statements in this analysis section without referring to the data once. You can't do that." He pointed out specific examples. TJ and Dave had written, "We found that most of the recorded storms began in the Atlantic Ocean, east of the Caribbean and made a C-like shape towards the United States and finished back east of the northern United States." He pushed them to "show/prove this [was] true" by showing "how many (and then, what %) of the storms had this 'C-shape' path." He pointed out how they could classify each storm in the time period as having one of a set of path shapes, such as the C-shape they mentioned.

For their revised report, the boys took up many of their teacher's suggestions, thus completing the transformative communication sequence. They categorized each storm as having one of three path shapes and gave the number of storms within each category from among the 83 storms over the period. They also produced a pie chart showing that 51% of the storms followed the C-shape, 22% a "straight-C," and 27% "irregular." The Hurricane group's revised report was a significant improvement over their first draft, with conclusions supported specifically by data analysis.

As with the group who did the project on plesiosaurs, Dave and TJ needed two tries at the third and fourth step in the transformative communication sequence, negotiating the meaning of the teacher's transformation of their idea and putting it into practice, before they could effectively appropriate the idea. In Dave and TJ's case, the second attempts at Step 3 took place in the form of an "action feedback dialogue" (Polman, in press) on their previously written-up analysis, and in Step 4 was implemented in their revised report. In addition, the transformative communication took place through a combination of written and oral verbal exchanges. In addition to the repetition in the second try and Wagner's greater specificity, the stability of Wagner's written comments as compared to his oral suggestions may P A G E P R O O F S have been necessary for the students to glean his intended meaning given their lack of expertise at these scientific practices.

MOONS: TRANSFORMING AN UNSUPPORTED CLAIM INTO A GRAPH OF TWO VARIABLES

For their project, Rich and Steve compared and contrasted moons in our solar system. They gathered data on various characteristics of moons, such as density, size, mass, and orbital period, and meticulously organized the data in tables and graphs-a separate graph for each variable. In numerous conversations and comments on interim milestones, Wagner pushed them to think about questions their data could illuminate, such as why the moons were different from one another or what the connections were between variables. But the students had difficulty in finding patterns.

The crucial exchange began when Rory received Rich and Steve's final research report. The students had included only graphs of single variables and then listed each graph's interpretation separately. For instance, they included a line graph showing each of the moon's orbital time period and a bar graph of each moon's density. In the text, the students wrote, "The graph [of orbital period] shows that Earth's moon has the longest orbital period, 27.32 days, while Miranda has the shortest orbital period, 1.4 days." Similar graphs in different styles were included for mass, surface temperature, and distance from planet. In the Data Analysis section of the paper, Steve and Rich did not describe any relationships between variables, except in the statement that "Titan has a short orbital period in relation to its mass"-a statement they did not choose to elaborate. But at the very end of the paper, buried in the Conclusion, they wrote something more like a testable claim: "We have come [to] the conclusion that both Titan and Earth's moon [have] a much greater mass and density than Miranda, and that this could be why both Titan and Earth's moon have longer orbiting time periods." Wagner seized this claim about how mass and density could be related to the orbital period of the moons and showed Rich and Steve how they could directly test it by graphing, for instance, density on the y-axis and time period on the x-axis.

Once again, Wagner perceived that the students' work could be transformed to a more successful move in the game of science than they themselves were originally aware. Like the group who did the Hurricanes project, Rich and Steve had developed a sense that a relationship existed in the data-that is why they put the comment in the conclusion-but they did not know how to present their data to back up a claim. In both cases, a clear analysis technique may be difficult to find even after a general impression has been reached by working with the data. Wagner's greater experience enabled him to see that a graph of one variable against the other would enable the students to directly check their claim that the two variables covaried. When graphed, it appeared that in the students' data, a relationship between density and orbital period, but not between mass and time period, was supported. Using similar methods, Wagner suggested that the students could create combination graphs for all the possible pairs of variables from their separate graphs. In this way, another apparent linear relationship was revealed-between the mass of a moon and its distance from the planet.

When Steve and Rich got the final version of the paper back, they were excited, because, as Steve put it, they "finally saw, you know, what [we] were trying to find,

P A G E P R O O F S

with the patterns." Although there was no provision for revising their paper again, the students got a chance to use the insight in their presentation to the class the following week. Steve and Rich created graphs of their own using Wagner's sketches as a model. In their presentation, they used the line graphs of two variables to support their claims, such as the one that "if a moon has a greater mass, that might affect its distance from the planet that it comes from." With statements about one factor "contributing to" or being "affected by" another, Rich and Steve had finally moved into the realm of making empirically warranted causal arguments, albeit tentative and somewhat awkwardly stated ones. As in the scientific community, they were making their claims with the aid of particular types of inscriptions-in this case, somewhat crude graphs. The graphs made their claim more compelling and understandable [START_REF] Gordin | The Climate Visualizer: Sense-making through scientific visualization[END_REF][START_REF] Latour | Drawing things together[END_REF]. Steve and Rich had a great deal to learn about analyzing data, but transformative communication helped them to begin making progress.

MUTUAL INSIGHTS THROUGH CONVERSATION WITH ONE ANOTHER AND THE SITUATION

For effective teaching and learning, it is not enough for teachers to simply tell students what to do. Wagner wanted to ensure that students participated in research design and the selection of analysis techniques so that they could learn about research design and analysis strategies. This contrasts to traditional "cookbook" labs, which take such decisions out of the hands of students and consequently preclude opportunities for deeper learning likely to lead to autonomous action in the future. But involving students can be time consuming and difficult. The difficulty and pitfalls of student participation in the whole process of research has been recognized by a number of student-scientist collaborative efforts, but even though it is often messy from scientists' perspective to have students involved in the whole process, it is educationally significant [START_REF] Pea | Science education as a driver of cyberspace technology development[END_REF]. Transformative communication can prove useful in maintaining this balance between student ownership and the teacher finding ways to guide students in potentially promising directions, as both parties make crucial contributions. As Rory described it, Sometimes [students] come up with things that are really creative that I would have never thought about, which then leads me to think of other things that might be do-able. And sometimes- [and] this gets in to the negotiating thing-sometimes they get real close to something, or have a neat idea, but it's not do-able, so then, how do you turn that into something that is do-able? Sometimes they do it, [and] sometimes I can do it.

And in some cases like those detailed earlier, the students and teacher can truly do it together. In the interactions described, the teacher helped the students transform the moves they made in the research process into more sophisticated moves that neither he nor the students would have originally predicted, thus leading to mutual insights. The interactions can take place over an extended period of time, in real-time or written discussions, but the important thing is that both teacher and student participation contributes. To borrow a phrase from Donald [START_REF] Schön | The reflective practitioner: How professionals think in action[END_REF], the process of transformative communication enables both Rory and his students to "engage in a conversation with the situation which they are shaping" (p. 103). In

P A G E P R O O F S

this case, it also allows them to engage in a conversation with each other. Whereas Schön was talking about reflective practitioners of design, such as architects, working alone, the process is remarkably analogous in these social interactions between teacher and student. Like architects who find "new and unexpected meanings" in drawings they create, Wagner and his students sometimes found new and unexpected meanings in the changes they produced in one another's interpretations and the situation. As Wagner stressed to his students, they did know important and useful things about their topic and data as they conducted their inquiry, but he often needed to help them conceptualize how what they knew could be used to accomplish scientific inquiry.

In these cases, the "project unit activity structure," with its set of interim milestones that Wagner designed for conducting projects and "verbal exchange activity structures" such as action negotiation dialogues and action feedback dialogues (Polman, 2000, in press), helped him to support students through transformative communication. The project unit activity structure set up the students' desire to formulate a researchable question or an analysis strategy that would help them to answer their question, and Rory made suggestions in verbal exchanges that helped students see how the work they had done and knowledge they had gained could help them get to the next stage in the project. As Wagner observed, students learn in projects on a need-to-know basis: "They won't care [about data analysis strategies] until they have to do it." But when faced with taking their project to the next step, they more readily recognized the value of Wagner's insights.

CONCLUSION

Project-based science teaching and learning involve complex role changes for teachers and students. Too often, the complex work teachers perform as facilitators and guides for project-based student work is left mysterious. In this chapter, we described a dialogue sequence for transformative communication, one productive discourse strategy teachers can use in the role of facilitator. We also elaborated concrete cases in which this strategy was used successfully to help students accomplish science inquiry with more sophistication than they could originally conceive. When teachers set up project activities that challenge and scaffold students in carrying out authentic elements of science practice (National Research Council, 2000;[START_REF] O'neill | Why educate "little scientists?" Examining the potential of practice-based scientific literacy[END_REF], the students will develop numerous seeds of scientifically interesting and rigorous inquiry. But as the learning paradox teaches us, the seeds alone do not have what is needed to enable the production of new knowledge. The environment the seeds are planted in must be fertile. The seeds need the sunlight of teacher's more expert vision to reveal their potential, and the soil and water of interaction between teacher and students, before they will sprout to reach their full potential.

  P A G E P R O O F Svoice and understanding of the initiate. Each participant potentially provides creative resources for transforming existing practice.(p. 288)

  Rory: OK, what do you want to do? Bruce: We want to show UFOs are alien space ships. Rory: [doubtfully] Any ideas on how? Bruce: I don't think there's any way to prove it unless they saw the alien in there and they waved at them. That's the only evidence there is. Rory: Right. That's the problem. Cheryl: I don't see why we can't write a report on it if people have written whole books on it. [Cheryl interpreted the project at this point as essentially the same as an extensive report for an English class. As time went on, she began to grasp the importance of using empirical data to support a claim.] Rory: [does not directly address Cheryl's confusion at this time] You know, Joe [Polman] and I were talking about the analysis Condon did that you wrote about in your background information [report]. It was interesting because Condon claimed to have explained the sightings with known phenomena. [For your project] you could verify what somebody like Condon has done.

TABLE 12 .1 Dialogue Sequence for Transformative Communication

 12

	(1)

TRANSFORMATIVE COMMUNICATION

ACKNOWLEDGMENT

The authors are grateful to the National Science Foundation, which supported this research of the CoVis Project (archived at: http://www.covis.nwu.edu/) under grants RED-9454729 and MDR88-55582. A grant from the James S. McDonnell Foundation supported the first author 's completion of this chapter.


Fátima L Mota

António J Queimada

Alfonsina E Andreatta

Simão P Pinho

Eugénia A Macedo
email: eamacedo@fe.up.pt

Calculation of Drug-Like Molecules Solubility using Predictive Activity Coefficient Models

Keywords: A-UNIFAC, Complex chemicals, Modelling, NRTL-SAC, Solubility, UNIFAC

The A-UNIFAC, UNIFAC, and NRTL-SAC models are used to predict solubility in pure solvents of a set of drug-like molecules. To apply A-UNIFAC, a new set of residual interaction parameters between the -ACOH group and six other groups had to be estimated. The solute model parameters of NRTL-SAC were also estimated for this set of molecules. NRTL-SAC showed better performance at 298.15 K, with an average absolute deviation of 37.6%. Solubility dependence with temperature was also studied: all models presented average deviations around 40%. In general, there is an improvement given by the A-UNIFAC over the UNIFAC in aqueous systems, proving the importance of taking association into account.

The reference solvent approach was also applied improving the results. Solubility in pure solvents can now be predicted with an average deviation around 35.2%. This approach reduces differences previously found between the three models, being a powerful methodology.

Introduction

Solubility has been recognized as one of the most important properties for designing separation and purification processes of complex molecules, such as biomolecules and active pharmaceutical ingredients [1,2]. In many cases, data are unavailable due to reduced amounts of sample, time limitations, or inherent complexities with experimental measurements. In such cases, the increasing interest and importance of solubility modelling is clear, as can be seen in the very recent works of Ellegaard et al. [3] and Diedrichs and Gmehling [4].

The Non-Random Two-Liquid (NRTL) Segment Activity Coefficient (SAC) is a recent and successful model for solid-liquid equilibrium calculations, and the idea behind is to limit the number of intermolecular interaction parameters [5,6]. This model was successfully employed for complex chemicals where acceptable deviations were obtained between experimental and predicted values: average root mean square error in ln x of 0.37, what corresponds to ±45% of accuracy in solubility predictions [5][6][7][8].

The group-contribution methods, like UNIFAC [9,10] and A-UNIFAC [11,12] are adequate techniques to provide reasonably accurate estimates of fluid mixtures nonidealities. Gracin et al. [13] used UNIFAC to predict drug solubilities in pure solvents, but the results were not accurate enough to allow the design of crystallization processes, or the selection of solvents. It is well known that UNIFAC method is not suitable when strong association effects are present. In order to take them into account, an extended version, the A-UNIFAC, was presented by Mengarelli et al. [14], being successfully applied to mixtures containing sugars, alcohols, water, carboxylic acids, esters, aromatic hydrocarbons and alkanes [11,12,15].

Avoiding the knowledge of the solute melting properties, the reference-solvent approach (RSA) [1,16,17] is an interesting alternative for predicting solubilities of solids. It minimizes the impact of the melting data uncertainties, being so interesting when there is a decomposition reaction, or solid-solid or glass transitions, and allows to fit a small number of unknown parameters from a limited set of well-chosen experimental data. However, it involves the selection of a reference solvent, relative to which all solubility calculations are made. This methodology was used to study the solubilities of drugs in pure solvents [1], and of complex medium-sized chemicals in mixed solvents [16], and the results are promising even in the cases of relatively high solubility compounds where it is not expected.

The aim of this work is to evaluate different activity coefficient models, UNIFAC, A-UNIFAC and NRTL-SAC, for solubility calculations of drug-like molecules, predicting how solubility vary with solvent type and temperature. With the application of RSA, the impact of calculating solubility without explicitly using pure component properties was checked. For that purpose, an evaluation database constituted by compounds with different functional groups and molecular sizes, showing a multiplicity of interactions in different solvents was compiled. They are benzoic acid, salicylic acid, acetylsalicylic acid, ibuprofen, hydroquinone, estriol and estradiol (Figure 1). An extension of the group interaction parameters available for A-UNIFAC was needed, and the solute parameters of the NRTL-SAC model were also estimated. The number of solutes and solvents involved extends considerably previous studies, allowing to understand their usefulness to predict solubility of pharmaceuticals.

Modelling

The solubility of a solid solute in a liquid solvent can be calculated by solving the thermodynamic equations of equilibrium [START_REF] Prausnitz | Molecular Thermodynamics of Fluid-Phase Equilibria[END_REF]. In Appendix A, the most important equations of the three models used in this work are briefly presented. The required pure solute properties are given in Table 1.

New A-UNIFAC group interaction parameters

For the group-contribution methods, the volume and area parameters were based on the Gmehling et al. [24] revised UNIFAC tables. The residual group interaction (a m,n ) and association parameters used in A-UNIFAC method were published by Ferreira et al. [12], while those used in UNIFAC method were based on Poling et al. [START_REF] Poling | The Properties of Gases and Liquids[END_REF] tables. The chemicals have the following associative groups: salicylic acid has carboxylic, hydroxyl and aromatic ring; benzoic acid and ibuprofen have carboxylic and aromatic ring; acetylsalicylic acid has carboxylic, ester and aromatic ring; hydroquinone, estriol and estradiol have hydroxyl and aromatic ring. In the majority of the studied systems, both solute and solvent can associate, like in alcohols and aqueous systems. Benzene derivatives and esters can only associate if the solvent has an electropositive site.

However, to apply the A-UNIFAC method, it was necessary to extend the residual group interaction parameters available [12]: the unknown parameters involving the -ACOH group were estimated to represent molecules such as salicylic acid, hydroquinone, estriol and estradiol. The association in this group is assumed to be the same as the association in the -OH group, given by Ferreira et al. [12], but the residual group interaction parameters were estimated using experimental data on low-pressure vapor-liquid equilibria (VLE) of binary mixtures and liquid-liquid equilibria (LLE) of ternary mixtures. Table 2 shows the database used in the fitting procedure. The residual parameters for ACOH/ACH and ACOH/CH 2 were first calculated using VLE data of phenol-benzene and phenol-alkanes, respectively, while the residual parameters for ACOH/H 2 O, ACOH/OH, ACOH/COOR, ACOH/COOH interactions were determined simultaneously using all other data expressed in Table 2. Table 3 reports the new estimated group interaction parameters for -ACOH between paraffinic, aromatic, alcohol, water, ester and acid groups.

Table 4 lists the average deviations obtained in the correlation of binary VLE data using the A-UNIFAC method. The results are satisfactory, even if for water-phenol system higher deviations were found. In fact, in order to obtain a good description of both VLE and LLE equilibria a compromise had to be considered when estimating the ACOH/H 2 O parameter. As can be seen in Figure 2, an accurate description of the LLE for the water-phenol-benzene system was achieved using the same set of parameters for both types of equilibria.

New NRTL-SAC solute parameters

To apply the NRTL-SAC model, the solute parameters had to be estimated using solubility data in pure solvents at 298.15 K [6]. In Table 5, the conceptual segment numbers found for each solute are presented, as well as the number of solvents used for each solute. Using these parameters, the model can be used to obtain the solubility of the same solutes in different solvents, using the solvent parameters reported in the literature [6]. Even if some outliers are found, an average deviation of 41% is obtained in the parameters estimation, with a maximum deviation of 67% for estriol.

Reference Solvent Approach

To apply the RSA, all the required parameters are known, and no data fitting is required. According to this methodology, the solubility in a solvent i can be calculated as far as the solubility in a solvent j and an activity coefficient model are known:

i j j i x x 2 2 2 2 ln ln ln ln γ γ - + = (1)
The selection of the reference solvent (j) is based on the minimization:

∑ + - + i i i j j j NP x x 2 2 2 2 ln ln ln ln min γ γ (2)
where NP is the total number of data points for the different i solvents in the database.

Results and Discussion

In order to compare the performance of each model, the absolute average deviations (AAD) were calculated. In the following sections, the results are analysed in terms of solubility at 298.15 K, its temperature dependence and, finally, the important features of the RSA methodology.

Solubility at 298.15 K

Table 6 shows the average AAD's for the solubility calculations in pure solvents at 298.15 K. For comparison, the experimental mole fraction ranges are also presented.

The averages presented at the bottom of the table are weighted means, taking into account the number of solvents studied for each solute. It is important to mention that whenever the AAD is higher than 150% in a given solvent, this is excluded from the average presented in all the models. More than 70% of the outliers were found in the calculation of the solubility in water, alkanes or aromatic solvents.

For salicylic acid [47], UNIFAC and NRTL-SAC models perform almost similarly, being acetic acid the only solvent for which the UNIFAC method is significantly better. Comparing group-contribution methods, A-UNIFAC is better than UNIFAC in the case of water solubilities, confirming that UNIFAC work poorly with aqueous systems. However, the results found with NRTL-SAC in water are still better than those found with the cubic-plus-association equation of state by Mota et al. [48] The three models are reliable for the calculation of benzoic acid solubilities in pure solvents. The AAD is particularly high in n-pentane with UNIFAC and NRTL-SAC, but A-UNIFAC performs well.

Excluding the esters, for acetylsalicylic acid containing systems, the NRTL-SAC model presents better results than the group-contribution methods, but for many solvents a fair comparison is hampered by the inexistence of NRTL-SAC parameters.

A-UNIFAC adds an improvement over UNIFAC for all the studied solvents. The deviations found by Charlton et al. [49], applying the Abraham general solvation model, are in the same order of accuracy of NRTL-SAC.

For ibuprofen [50,51], the results obtained in this work are better than those obtained by Stovall et al. [51] with the Abraham general solvation model, excepting 1butanol and 1-propanol.

The data reported by Ruelle et al. [23] for estriol were better predicted using the UNIFAC method, but the set of solvents studied is too reduced for a definite conclusion. Concerning the NRTL-SAC model, the number of solvents used for parameter estimation was in accordance with the value suggested by Chen and Crafts [6], presenting a variety of interaction characteristics that would be appropriated to estimate the solute parameter with some physical meaning. Even if the magnitude of the parameters depends on the number and type of solvents, the hydrophobic segment is null, while in the estradiol molecule it is an important segment, although these two molecules are very similar. This is maybe an aspect interfering in the quality of predictions. Bouillot et al. [8] developed a method to choose the best solvents for solute parameters regression. NRTL-SAC and UNIFAC revealed better performance in the calculation of the data of estradiol solubility in pure solvents at 298.15 K [23]. In Figure 3, the importance of having an activity coefficient model to calculate estradiol solubilities at 298.15 K is shown. As expected, the ideal solubility is in high disagreement with experimental solubilities since the solute-solvent interactions are not taken into account.

Figure 4 presents a comparison between the group-contribution methods for molecules presenting the -ACOH group and the other solutes: the results worsen as long as the number of associative groups increases, but both methods are able to represent solubility in the majority of the solvents studied. The estimation of the -ACOH residual parameter had strong influence, otherwise the results found with A-UNIFAC for hydroquinone, estriol, estradiol and salicylic acid would be much poorer.

Solubility Data as Function of Temperature

Whenever available, the solubility data as function of temperature were also analyzed. Table 7 shows the AAD's for these calculations taking only into account the solvents for which all the three models were used. The global AAD's are in accordance to those found for pure solvents at 298.15 K.

For salicylic acid [48,[52][53][54][55], UNIFAC is better for all studied systems, except in water where only NRTL-SAC calculates reasonably these solubilities. A-UNIFAC is still better than UNIFAC for aqueous solubilities.

For benzoic acid [56][57][58], except in the case of aqueous solubilities where UNIFAC is better, the three models perform almost similarly (A-UNIFAC is slightly better, with average AAD of 15.6%). The solubilities in octanol are presented in Figure 5 where the AAD found with A-UNIFAC is 13.5%. The results obtained by Qingzhu et al. [57] for benzoic acid in 1-octanol with the Wilson and λH equations correlate the experimental data as well as the NRTL-SAC predictions in this work. The results found by Wang et al. [58], with the NRTL, for the solubility in acetic acid are not too much different from the calculated by group-contribution methods, what puts into evidence the results calculated here because correlation and prediction are compared.

For the solubility data of acetylsalicylic acid, NRTL-SAC was the best model for the simplest alcohols, ethanol and 2-propanol [21]. The results found for these alcohols by Maia and Giulietti [21] with the Nývlt model, which is a correlative model with three adjustable parameters, are as good as the obtained with NRTL-SAC model. For the aqueous solubilities, NRTL-SAC is the best, but A-UNIFAC leads to a great improvement over UNIFAC: AAD from 87.0 to 14.8%. NRTL-SAC gave good estimates of ibuprofen aqueous solubilities where the others fail. Except ethyl acetate and propylene glycol, for all the other solvents A-UNIFAC originates better predictions. The results with A-UNIFAC were better than those reported by Hanhnenkamp et al. [59] with UNIFAC, modified UNIFAC or COSMO-RS models.

For hydroquinone containing systems [60], the UNIFAC and NRTL-SAC results are better, except in water where A-UNIFAC is the best. For hydroquinone, the estimation of -ACOH group interaction parameters for A-UNIFAC method had a great importance: if the group assignment was considered to be -AC + -OH instead, the method shows special difficulties to deal with alcohols and esters, presenting deviations around 90%; with the proper molecule division, with an -ACOH, the method is perfectly able to represent those solubilities.

Analyzing the estradiol data as a function of temperature [61], A-UNIFAC gave better results in cyclohexane and benzene, while NRTL-SAC is better in ethanol.

Even if for some systems the results achieved were not satisfactory, the improvement obtained by considering an association term in the A-UNIFAC comparing with the original UNIFAC is shown in Figure 6 for all the aqueous solubilities studied in this work. In fact, preliminary studies developed for solubilities in mixed solvents containing water have shown the same trend, which is important for this type of solutes.

Reference Solvent Approach

An evident problem arising from the use of solubility equation is the need of solute liquid and solid heat capacities, and melting properties, which usually are not available present large discrepancies in the open literature. In this way, the solubility data at 298.15 K were analyzed using the same activity coefficient models together with the RSA. Whenever the RSA was applied, no further model parameters are estimated. Table 6 reports the AAD's for the solubility calculations in pure solvents at 298.15 K, where it is also presented the weighted average for each model and the reference solvent. It must be mentioned that in a small number of cases (benzoic acid and ibuprofen with UNIFAC, estradiol with A-UNIFAC and NRTL-SAC, and acetylsalicylic acid with NRTL-SAC) the application of the models without the RSA gives better results, but the differences are minor.

In general the results improve significantly after applying RSA, and this approach also eliminates the AAD differences previously observed between models. This is a clear advantage of this methodology because the melting properties, which are a source of inconsistencies, are eliminated.

It should be referred that with NRTL-SAC model, the reference solvent is always an alcohol, while with UNIFAC an alcohol or an ester is found. In fact, excepting the acetylsalicylic acid with UNIFAC, and ibuprofen with the NRTL-SAC, the solvents found to be the reference already presented good performances without RSA. In the selection of the reference solvent type for the A-UNIFAC method, establish a definite pattern is more difficult.

Conclusions

The compounds under study are complex medium-sized chemicals with different structures and functional groups, with different affinities to associate. Groupcontribution methods were compared with the NRTL-SAC model to predict their solubility data in pure and mixed solvent systems. In order to extend the A-UNIFAC method to the associating molecules under study, VLE and LLE data were used to extend the residual parameter table: new residual interaction parameters between the -ACOH group and several other were estimated. For NRTL-SAC model, four parameters had also to be firstly correlated for each solute.

In general, NRTL-SAC is able to correlate and predict solubility data for the studied systems. For aqueous systems A-UNIFAC was in general superior to UNIFAC, proving the need of taking into account the association effects. The results obtained with the reference solvent approach were almost similar for all the models; the improvement relatively to the results without this methodology is in general significant, proving its usefulness.

Therefore, if drug solubility estimates are needed, for systems in which data in a set of selected solvents are readily available, it is suggested to apply the NRTL-SAC model. For solutes where experimental solubility data are not available or difficult to obtain, and if all the group parameters are known, the application of UNIFAC method with the reference solvent approach is a valid option. The combinatorial term, is:

∑ - + + = J J J I I I I I I I I C I l x x l q z x φ φ θ φ γ ln 2 ln ln (A2)
where θ I and I φ are the area and volume fractions of component I, and similarly to the variable l I are defined by equations found elsewhere [62], z is the coordination number (set equal to 10) and q I is the area parameter of component I. The residual term, is:

( ) ( ) ( ) ∑ Γ - Γ = k I k k I k R I ln ln ln υ γ (A3)           -       - = Γ ∑ ∑ ∑ m n nm n km m m mk m k k q ψ θ ψ θ ψ θ ln 1 ln (A4)
where k Γ is the residual activity coefficient of group k, ( )

I k
Γ is the residual activity coefficient of group k in a reference solution containing only molecules of type I, ( )

I k
υ is the number of group k present in molecule I and mk ψ is a binary interaction parameter [9,62].

In order to take the association effects into account, an extended version of UNIFAC, the A-UNIFAC, was presented by Mengarelli et al. [14] The association activity coefficient term is a function of the fraction of non-bonded sites in the solution (

∑ ∑ ∑ =                   ∂ ∂       - +         - +         = NGA k A A n P T I A k A A A I A I A I k assoc I k k j k k k k k k n X N X X X X X 1 , , 2 1 1 2 ln ln ϑ γ (A5)
where N k is the number of moles of associating group k, I k ϑ represents the number of groups of type k in a molecule of component I, n I is the number of moles of component I, NGA is the number of associating groups and A k is the associating site of group k. The fraction of non-bonded sites is a function of the associating strength ( )

j k B A ∆ between site
A of group k and site B of group j and the associating group density in the mixture ρ j [12,14]:

∑ ∑ = = = NC I I I NC I i I j j x r x 1 1 ϑ ρ (A6)
where NC is the number of components in the mixture and r I represents the UNIQUAC molecular volume of species I (evaluated from UNIFAC group volume parameters R k ).

The associative compounds are represented by specific associating groups: the one-site carboxylic group, which can self-and cross-associate; the two-sites hydroxyl group, which can also self-and cross-associate; the one-site ester group and one-site aromatic ring, which can only cross-associate with electropositive associating sites.

The Non-Random Two-Liquid Segment Activity Coefficient model [5,6] (NRTL-SAC) is an activity coefficient model where the liquid non-idealities are described in terms of four types of segments: hydrophobic (X), polar attractive (Y-) and repulsive (Y+), and hydrophilic (Z), to account for several interactions. The activity coefficient is obtained from the sum of a combinatorial ( ♦, hydroquinone [60]; ▲, estriol [23]; ■, estradiol [23].

2 A

 2 Nomenclature a m,n = residual group interaction parameter (g/mol) M = molar mass (g/mol) NC = number of components in the mixture NP = number of data points NS = number of solvents P = pressure (Pa) T = absolute temperature (K) x = mole fraction X = hydrophobic segment in NRTL-SAC model Y+ = polar repulsive segment in NRTL-SAC model Y-= polar attractive segment in NRTL-SAC model Z = hydrophilic segment in NRTL-SAC model Greek Symbols γ = activity coefficient ∆C p = difference between the heat capacity of the pure liquid and solid (J/mol.K) ∆ fus H = fusion enthalpy (J/mol) -UNIFAC = modified UNIFAC method which takes account association LLE = Liquid liquid equilibria NRTL-SAC =Nonrandom two-liquid segment activity coefficient model RSA = reference solvent approach UNIFAC = UNIversal quasi chemical Functional-group Activity Coefficients method VLE = Vapor liquid equilibria Appendix AIn the UNIFAC method, the activity coefficient is obtained from a combinatorial ( C I γ ) and a residual ( R I γ ) contributions[9,62]:

  where I and J are component indexes, m is the segment based species indexes, r m,I is the number of segment species m contained in component I, r I is the total segment number of component I, φ I is the segment mole fraction of component I, lc m Γ is the activity coefficient of segment species m, I lc m , Γ is the activity coefficient of segment species m contained only in component I.

Figure 1 .

 1 Figure 1. Chemical structures of the compounds under study.

Figure 2 .

 2 Figure 2. LLE of water-phenol-benzene at 298.15 K: •, experimental[39]; -, A-UNIFAC method.

Figure 3 .

 3 Figure 3. Estradiol mole fraction solubility at 298.15 K [23] calculated by different

Figure 4 .

 4 Figure 4. Comparison between group-contribution methods at 298.15 K: closed

Figure 5 .

 5 Figure 5. Benzoic acid mole fraction solubility in 1-octanol (♦) as a function of

Figure 6 .

 6 Figure 6. Comparison between group-contribution methods for aqueous solubilities at

Figure 1 :

 1 Figure 1:

Figure 4

 4 Figure 4:

Figure 5 :

 5 Figure 5:

Table 1 . Pure solute properties.

 1

	Solute	T m (K)	∆ fus H (kJ/mol) ∆C p (J/mol.K)	M (g/mol)
	Salicylic acid	432.0 a	24.6 a	37.0 b	138.1
	Benzoic acid	395.5 c	17.5 c	40.9 b	122.1
	Acetylsalicylic acid	416.2 d	29.8 d	26.6 b	180.2
	Ibuprofen	347.2 e	25.5 e	50.3 e	206.3
	Hydroquinone	445.5 b	27.1 b	26.7 b	110.1
	Estriol	555.0 f	42.7 f	----	288.4
	Estradiol	445.0 f	40.6 f	----	272.4
	a [1]; b [19]; c [20]; d [21]; e [22]; f [23].

Table 2 . Database used for the estimation of A-UNIFAC residual group interaction parameters.

 2

	i	j	System	C atoms	NP Type of	T range	P range	Ref.
				in groups		data	(K)	(bar)
	ACOH	ACH	Phenol + benzene	-	133	VLE	323-449	0.005-2.6	[26-31]
		CH 2	Phenol + alkane	C 8 , C 10	31	VLE	383-393	0.09-0.64	[26]
		H 2 O	Phenol + water	-	103	VLE	288-455	0.02-1	[32-38]
			Phenol + water +	-	10	LLE	298	1	[39]
			benzene
		OH	Phenol +	-	20	VLE	376-392	0.12	[40,41]
			cyclohexanol
			Phenol + water +	C 4 -C 5	40	LLE	298-313	1	[42,43]
			alcohols
		COOR	Phenol + esters	C 4 , C 6 -C 7	67	VLE	362-465	0.26-1	[34,44]
			Phenol + water + ester C 2 , C 4 , C 6	99	LLE	298-318	1	[39,43,45]
		COOH	Phenol + acids	C 3	26	VLE	383-403	0.08-0.70	[46]
			Phenol + water + acid	C 9	9	LLE	298	1	[39]

NP: number of experimental points.

Table 3 . New A-UNIFAC residual group interaction parameters a m,n (K).

 3

	M	n	a m,n	a n,m
	ACOH	CH 2	343.4	-55.40
		ACH	74.03	-42.87
		OH	-722.6	-410.1
		H 2 O	-355.0	-179.2
		COOR	-756.7	12.03
		COOH	402.9	1028

Table 4 . VLE calculations: average deviations in compositions

 4

	(δ δ δ δy) and pressure

Table 5 . NRTL-SAC molecular parameters (r m,I ) for the studied compounds and number of solvents used (NS).

 5

	Solute	NS	X	Y-	Y+	Z
	Salicylic acid	26	0.886	1.841	0.372	0.444
	Benzoic acid	26	0.316	0.046	1.876	0.580
	Acetylsalicylic	16	0.508	0.219	0.009	1.000
	Ibuprofen	28	0.789	0.104	1.837	0.107
	Hydroquinone	7	0.243	1.915	1.749	0.020
	Estriol	10	0.000	0.003	0.037	1.216
	Estradiol	24	1.087	0.001	1.317	1.463

Table 6 . AAD's a,b (%) for solubility modelling in pure solvents at 298.15 K, experimental solubility range, and respective reference solvent when RSA is applied.

 6

						AAD (%)
		NS	Xexp range	A-UNIFAC	A-UNIFAC + RSA	UNIFAC	UNIFAC + RSA	NRTL-SAC	NRTL-SAC + RSA
	Salicylic acid	12 [1.5 x 10 -4 ; 0.21]	36.5	29.8 2-methyl-1-propanol	18.9	19.0 Ethyl acetate	18.4	15.7 1-butanol
	Benzoic acid	14 [5.9 x 10 -3 ; 0.20]	24.0	23.0 Benzene	29.7	30.5 Ethyl acetate	27.9	14.1 1-butanol
	Acetyl			74.1	30.8	79.6	31.2	31.3	36.3
	salicylic acid	26 [1.0 x 10 -3 ; 0.09]		2-methyl-1-butanol		2-methyl-1-propanol		1-octanol
				40.0	40.4	31.5	40.3	59.6	58.9
	Ibuprofen 19 [9.9 x 10 -7 ; 0.34]		cyclohexane		Isopropyl myristate		1-pentanol
	Estradiol 6 [5.9 x 10 -7 ; 0.02]	80.7	83.9 Ethanol	58.7	47.1 ethanol	55.6	68.4 ethanol
				51.2	35.7	47.6	32.7	37.6	37.1

a Average calculated without considering the outliers (AAD > 150%)

b Outliers -salicylic acid: acetic acid, water; benzoic acid: n-pentane; acetylsalicylic acid: benzene, methyl acetate; ibuprofen: benzene, acetic acid; estradiol: cyclohexane.

Table 7 . AAD's a,b (%) for solubility modelling in pure solvents as a function of temperature.

 7

			AAD (%)
		A-UNIFAC UNIFAC NRTL-SAC
	Salicylic acid	63.3	8.0	10.7
	Benzoic acid	15.6	25.7	19.3
	Acetylsalicylic acid	77.5	84.1	14.3
	Ibuprofen	40.0	45.1	72.3
	Hydroquinone	58.0	40.5	35.3
		55.7	23.1	21.8
		51.7	37.8	29.0

a Average calculated without considering the outliers (AAD > 150%)

b Outliers -salicylic acid: water; benzoic acid: water; hydroquinone: acetic acid, water; estradiol: cyclohexane, ethanol.

Acknowledgements

The authors are grateful for the support provided by Fundação para a Ciência e a Tecnologia (FCT, Lisboa, Portugal) and by LSRE financing by FEDER/POCI/2010. Fátima L. Mota acknowledges her FCT Ph.D. scholarship SFRH/BD/32372/2006.